Multi-objective Motion Planning Presented by Khalafalla Elkhier Supervised by Dr. Yasser Fouad

Research area Robot motion planning Multi Objective Enhanced Genetic Algorithm by modified the A* search algorithm. Other implementation for the MGA with A*.

Research area Problem : Multi-objective Motion Planning can be formalized as a Multi-objective optimization problem,involving more than one objective function to be optimized simultaneously Solution: A perfect multi-objective solution that simultaneously optimizes each objective function is almost impossible.

A reasonable solution to a multi-objective problem is to investigate a set of solutions, each of which satisfies the objectives at an acceptable level without being dominated by any other solution. A solution is called non-dominated, or Pareto optimal, if none of the objective functions can be improved in value without degrading some of the other objective values

Examples: In network design we are concerned with its cost, capacity, reliability; in investments we care about return and risk; in radiation therapy we care about the effects on the tumor on the one hand, and healthy organs on the other.

Definition: Zitzler and Thiele, 1999

Robot motion planning

Robotic motion planning is a promising study issue in the field of robotics. most significant research objectives can be categorized around attaining Safety Path length Future prediction Run time Control Less computation cost Accuracy Efficiency Smooth path Stability

Current research can be generally divided in two main methods: classical and heuristic. The classic approaches suffer from high time complication in high dimensions, and catching in local minima. Consequently, the application of the heuristic approaches was extended due to their achievement in addressing problems such as computational complexity, exploration and local minima.

ClassicalHeuristic. Artificial potential field (APF) Genetic algorithms RoadmapParticle swarm optimization Cell decompositionSimulated annealing Mathematical programming Neural networks, Ant colony optimization

Multi Objective Enhanced Genetic Algorithm by modified the search A* algorithm

First Paper : Multi Objective Optimization of Trajectory Planning of Non-holonomic Mobile Robot in Dynamic Environment Using Enhanced GA by Fuzzy Motion Control and A*

Objective : Enhance the searching ability of robot movement towards optimal solution state in static and dynamic environments, by minimizing travelling distance, travelling time, smoothness and security, avoiding the static and dynamic obstacles in the workspace.

Method: A new hybrid approach based on Enhanced Genetic Algorithm by modified the search A* algorithm and fuzzy logic system 1.A global optimal path with avoiding obstacles is generated initially.(Off-line) 2.Then, global optimal trajectory is fed to fuzzy motion controller to be regenerated into time based trajectory.(On-line)

Parameter specification:

The environment model : A closed workspace (indoor area) without and with different numbers of obstacles. This area is described by a 2D static map (20 × 20); the starting point is S=(1, 1), and the target point is T=(19, 19) for a path. The positions of the obstacles are randomly chosen. Shortcut or decreased operator: This operator will eliminate obstacles nodes from map at the beginning of the algorithm.

Initial population : classical method and modified A* is used for generating a set of the sub optimal feasible paths in simple map and complex map, respectively. Then, the paths obtained are used for establishing the initial population for the GA optimization.

The A* algorithm fitness function. F(n) =( g(n)+ h(n)). In the study the accumulated cost and heuristic cost are the Euclidean distance between two nodes. The robot selection of the next node depends on the minimum value of F(n).

The modified A* method F(n) =Rand*( g(n)+ h(n)). in order to avoid the use of shortest path which it could affect the path performance in terms of multi objective (length, security and smoothness) in initial stage.

Optimization by modified GA: A chromosome represents the path and its length varies depending on the case at hand. Start position P(x 0,y 0 ) =(1, 1) Via-points P(x 1,y 1 ) and P(x i+1,y i+1 ) Target position P(x n,y n ) =(19, 19)

All chromosomes will be evaluated by fitness function a chromosome with the minimum fitness has a considerably higher probability than the others to select and reproduce by means of GA operators in the next generation. These steps are repeated until the maximum number of iterations is reached

The total cost of fitness (or objective) function of feasible path P with n points is obtained by a linear combination of the weighted sum of multi objectives F 1 (P) is the total length of path F 2 (P) is the path smoothness F 3 (P) is the path clearance or path security F 4 (P) represents the total consumed time

ω‘s represent the weight of each objective. They are tuned through simulation and try and errors, with best found values

GA operators: Selection: Two parents randomly are selected based on their fitness by using the Roulette wheel selection method. Crossover Operator: Single point crossover is used. This operation results feasible paths, because the nodes before crossover point in the first parent and the nodes after crossover point in the second parent and in opposite, are valid nodes.

Mutation Operator: The parental chromosome is chosen according to selection method. The parents start and target nodes are not mutated. The mutation operation is done by selecting an intermediate node in the parent according to mutation probability. These nodes are chosen randomly to replace the mutated node.

Enhanced Mutation : It is served as a key role to diversity the solution population, we proposed to enhance mutation operator by adding traditional A* search method to mutation. The enhanced mutation method is used to avoid fall into a local minimum, improve and decrease the distance of the partially path, between two randomly points (i and j) included in the main path

Deletion operator: It proposed to eliminate the repeated genes (redundant) from an individual (path). For specific gene, the approach reversely check if this is equal to others and this is done for each gene

Sort operation: This operator sorts the chromosomes of population according to their fitness at each generation. The feasible chromosomes are organized in ascending order according to their fitness, and secondly, if a group of chromosomes has an equal fitness values, they are again sorted, in ascending order.

Fuzzy Motion Planning The proposed fuzzy controller contains an obstacle avoidance strategy. It has two inputs. The first input is the optimum velocity from the GA and the second one is the obstacle when the robot detects new moving obstacle in its path.

The output is the final velocity of the robot. The fuzzy control might control the robot speed based on detection of any dynamic object. Not only the robot it can reduce the speed in case the dynamic object gets more close to robot, but also the control has ability to increase the speed when the robot becomes safe away from the dynamic obstacle.

fuzzy membership functions for input velocity has 9 linguistic variables. (Z: Zero, VVL: very very low, VL: very low, L: low, Medium, H: High, VH: very high, VVH: very very high, Maximum). The second input has 5 linguistic variables ( No, Far, Medium, Close, Very Close). It should be noted that the input 2 is normalized. For the output 9 membership functions have been used (Z: Zero, VVL: very very low, VL: very low, L: low, Medium, H: High, VH: very high, VVH: very very high, Maximum).

Other implementation for the MGA with A*.

Second Paper: Towards a Heterogeneous Navigation Team of Aerial-Ground Robots Based on Fuzzy Image Processing

Method: The blimp robot will scan the environment to detect the GR and the obstacles. The fuzzy edge detection and the shape-color features technique have been used to scan the environment and detect the objects. These maps will send directly to the ground station which has the proposed approach using Enhanced Genetic Algorithm modified by the search A* algorithm to find the optimal trajectory and path for the GR.

Third Paper: Integrated Motion Planning and control of multi objectives Optimization and Multi Robots Navigation

Objective : The goal of this study is to drive multi mobile robots from the start point to the target point with the possible multi objective optimal path with avoiding the collision risk among them and the static obstacle in the environment

Method : The proposed model includes two stages: The first is motion planner, which used to generate multi objective optimal path and trajectory for each robot independently from the start to the goal position using the MGA with A*. The second one is motion controller, which used to establish a movement strategy to let the robots drive around with avoiding the collision with each other using Sugeno fuzzy controller

Five objective functions are used to minimize travelling length, time, smoothness, security and trajectory and to reduce the energy consumption for mobile robots by using Cubic Spline interpolation curve fitting for optimal planned path.

References : 1\ A Review on Motion Planning and Obstacle Avoidance Approaches in Dynamic Environments, Adv Robot, Autumn \Classic and Heuristic Approaches in Robot Motion Planning – A Chronological Review 3\Multi Objective Optimization of Trajectory Planning of Non-holonomic Mobile Robot in Dynamic Environment Using Enhanced GA by Fuzzy Motion Control and A*

4\Towards a Heterogeneous Navigation Team of Aerial-Ground Robots Based on Fuzzy Image Processing 5\Integrated Motion Planning and control of multi objectives Optimization and Multi Robots Navigation

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